[Guest]

Consider the following square

You are asked by an instructor to choose 5 numbers from the square and perform a single kind of mathematical operation on them, and to do this repeatedly...a different set of 5 numbers, the same kind of operation, and repeat. (e.g. you will select five numbers and add them all together, for example, and then repeat)

1) What easy-to-follow rule can you follow each time in choosing your 5 numbers that will ensure that the final result of your math (adding, multiplying, dividing, etc) will always be the same number?

2) What mathematical operation will you be performing each time on those 5 numbers? (add, subtract, multiply, divide, square, etc)

3) What is the number you will always get if you follow the rule from question 1 and the operation from question 2?

Caveat: by 'easy-to-follow', I mean that following the rule, prior to your math, will not itself include any math...thus "Pick five numbers that multiply together to get X" is not the correct answer, as this is not 'easy-to-follow'. Question 1 is asking for a rule for *picking* the numbers, not for manipulating them after you pick them.

Partial Hint if it's too hard:

You will be multiplying the five numbers each time.

[Guest]

No tries yet?

Maybe the math heads haven't woken up yet.

Here's something to keep you busy in the meantime:

Why do mathematicians confuse Halloween and Christmas?

Because Oct 31 = Dec 25

[Guest]

there's no rule on picking numbers? like a person can pick all 1 or the number has to be unique? or are u talking about picking 5 squares on the diagram?

[Guest]

Can't say I've tried every combination, but this rule has worked so far

each number is from a different row and column than the other numbers chosen

and the product is 1984

Edited January 14, 2009 by Cherry Lane

[Guest]

I agree with u Cherry, gj!

[Izzy]

I'm being haunted by 1984! Ahh!

[Guest]

there's no rule on picking numbers? like a person can pick all 1 or the number has to be unique? or are u talking about picking 5 squares on the diagram?

I thought about including something like that, but I thought it might make it too easy.

As it is, the instructor does specify that 1) you are to pick five "different" numbers, and that 2) the next time you will pick a different set of five numbers, and etc.

Those two requirements together, I think, prevent someone from picking, say, the 4 in the upper left corner five times. That's neither 5 'different' numbers when different is taken to mean 'number type', nor is it 'different' when taken to mean 'number token'. And even if you could do that, the second requirement means that you can't keep picking the same number, so at some point you'd run out of fours

Good job

Edited January 14, 2009 by brotherbock

[Prime]

I thought about including something like that, but I thought it might make it too easy.

As it is, the instructor does specify that 1) you are to pick five "different" numbers, and that 2) the next time you will pick a different set of five numbers, and etc.

Those two requirements together, I think, prevent someone from picking, say, the 4 in the upper left corner five times. That's neither 5 'different' numbers when different is taken to mean 'number type', nor is it 'different' when taken to mean 'number token'. And even if you could do that, the second requirement means that you can't keep picking the same number, so at some point you'd run out of fours

Good job

I don't see how the second requirement prohibits picking the same number more than once. One set of 5 numbers is different from another set, as long as any one of the set members is different. So you can pick 4 of the same numbers as before and then choose a different 5th number. There are 25!/(20!*5!) =53130 different sets of 5 numbers there. So the instructor should have mentioned that he/she wanted only 5 different sets.

That said, the interesting quality of the matrix is...

The numbers in all rows have the same proportion, so it is convenient to view the rows as:

0.40* {10, 20, 16, 40, 25}

0.25* {10, 20, 16, 40, 25}

0.20* {10, 20, 16, 40, 25}

0.10* {10, 20, 16, 40, 25}

0.31* {10, 20, 16, 40, 25}

Thus, as Cherry Lane noticed, as long as each row and each column member occurs exactly once in each set of 5, the product is the same, since all the factors are the same.

This is a nice number puzzle. But I don't think the hint to use multiplication was necessary -- it was a dead giveaway.

[Guest]

I don't see how the second requirement prohibits picking the same number more than once. One set of 5 numbers is different from another set, as long as any one of the set members is different. So you can pick 4 of the same numbers as before and then choose a different 5th number. There are 25!/(20!*5!) =53130 different sets of 5 numbers there. So the instructor should have mentioned that he/she wanted only 5 different sets.

The first requirement prohibits you from picking the same number (say, all 4's) five times...because there are not 5 tokens of any given number, so you can't have 5 different number tokens, and five 4's (from the same square) would not be different number types. So either way you view 'different', you can't get five of the same number from this puzzle.

You could get four 4's and one 5, yes. But is there a rule that would 'ensure' that you get the same result from different sets in this way? Eventually, you will run out of 'different' sets of 4's and 5's.

This is a nice number puzzle. But I don't think the hint to use multiplication was necessary -- it was a dead giveaway.

Thanks I agree that the hint wasn't necessary, but it was for non-math geeks